erweitern (sin(x)+xcos(x))^2

Lösung

erweitern

(sin (x) + x cos (x))^{2}

x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

Schritte zur Lösung

(sin (x) + x cos (x))^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(sin (x) + x cos (x))^{2} = sin^{2} (x) + 2 sin (x) x cos (x) + (x cos (x))^{2}

= sin^{2} (x) + 2 sin (x) x cos (x) + (x cos (x))^{2}

Vereinfache

sin^{2} (x) + 2 sin (x) x cos (x) + (x cos (x))^{2} : x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

= x^{2} cos^{2} (x) + x sin (2 x) + sin^{2} (x)

e x p an d \frac{d ^{2}}{d x ^{2}} (x^{4}) - 2 x (6 x - x^{2})

e x p an d \frac{6 x ^{2} - 9 x + 1}{( x - 1 ) ^{2} ( x + 1 )}

s im pl i f y (x - 5) (x + 5)

e x p an d 7 (π - 5)

s im pl i f y (x + y)^{2}